Bodies affedied by Friction* 1S7 
will be as a x aC , b x bC, c x cC, Sec. alfo the effed of the inertia 
of the correfponding parts of the body will be as A x aC\ 
B x bC\ C x cC% &c. Now when the whole furface of the 
bafe and mafs of the body are concentrated in P, the effect of 
the fridion will be as a 4- b + c + Sec. x CP, and of the inertia as 
A + B + C + &c. x CP 2 ; confequently ax aCy-bxbCy ex cC 
4. & c. : a + t)-\-c -y Sec. x CP :: Ax aQd 4- B x 30 4- C x cO 
4- Sec. : A 4- B + C 4- &c. x CP 1 ; and hence 
CP = 
A x -J- B x M~ -j- 0 X cC -f- <&c. x q ~J— t). c -J- Sc 
a X X bC +cxcC -f&c. xA + B -f C+&c. 
(if S = the fern 
of the produds of each particle into the fquare of its didance 
from the axis of motion, T — the dim of the produds of each 
part of the bafe into its didance from the center, r = the area 
of the bafe, t = the folid content of the body) . 
■1 X t 
PROPOSITION IV, 
Given the velocity with which a body begins to revolve about the 
center of its bafe , to determine the number of revolutions which the 
body will make before all its motion be defrayed \ 
Let the fridion, expreffed by the velocity which it is able to 
dedroy in the body if it were projeded in a right line horizon- 
tally in one fecond, be determined by experiment, and called F; 
and fuppofe the initial velocity of the center of fridion P about 
C to be a. Then conceiving the whole furface of the bafe and 
mafs of the body to be colleded into the point P* and (as has 
a 2 
been proved in Prop. II.) — will be the fpace which the body 
fo concentrated vyili deferibe before all its motion be dedroyed j 
B b z hence 
